Over three quarters of British people would accept refugees into their neighbourhood or home, the survey results show, and 70% say the government isn't doing enough to help.

Up and down the country ordinary people are doing what they can to show their support for refugees and to try to make day-to-day life a little more bearable for the tens of thousands of people stranded in Europe. These refugees have fled unimaginable horror, and now camped out in makeshift sites across the continent, they face disease, mental health problems, exploitation and abuse. All the while our political leaders squabble, turn their backs, abdicate responsibility, and with the language they use and campaigns they run do their utmost to try and promote a hostile environment for immigrants of any kind.

But what these survey results show is that we, the people, aren't buying it, and this is something I've seen first-hand. Over the last month I've been involved with a grassroots initiative run by a group of parents from a south London primary school, collecting clothes, sleeping bags, camping mats and other supplies urgently needed in the refugee camps in Calais and Dunkirk. We did the same in January, appalled by the conditions people were living in and the failure of leadership by our governments in dealing with the crisis, and on both occasions the response from the local community was incredible.

As well as coverage in local media, we had support from a community football club, pilates groups, churches, local politicians from all sides, and an array of high street businesses from barbers and fish and chip shops to launderettes, opticians and cafes. Not only did people from all across London give much needed items of their own, they started their own collections at work or school, came along to help sort and pack donations, contributed money, transport, storage space, skills, knowledge and even came across the Channel with us to volunteer at the warehouse run by Care 4 Calais and in the camp. Our second trip was last Sunday. In all, we have taken five vans and three car loads of donations and volunteers over to France.

These kind of initiatives are going on all over the place - there are local organisations successfully campaigning for their councils to take in refugee families and working to help them settle in, grassroots groups organising fundraising comedy or music nights and individuals from clowns to carpenters to cooks heading as far as Greece to volunteer in refugee camps.

And this support for refugees doesn't just come from the UK. Globally, 80 per cent would accept refugees in their country, city, neighbourhood or home and two out of three people think their governments should do more to help refugees fleeing war and persecution.

I met some of those refugees in Calais at the weekend. After dropping off all the donations at the warehouse, a couple of us went with Care 4 Calais volunteers to offer English classes in the camp. Most residents were busy going about their business and politely told us another time would be better, but eventually, after wandering around for a while, a group of Afghan and Pakistani men, all in their 20s, took pity on us and invited us to sit down on a old mattress acting as a sofa in front of their wood-and-tarpaulin shelter.

We took some flash cards depicting - somewhat incongruously - scenes of late 80s American domestic life out of the supermarket bag-for-life containing our teaching pack, and encouraged our new students to describe the pictures. There was some conferring over whether 'shelves' were 'cupboards' and how to pronounce 'carpet', but their English turned out to be excellent, and the conversation quickly turned to why they were in the camp.

"There is no way to live in Afghanistan," said Said. "If you work for the government, the Taliban and Daesh come after you. If you work for the Taliban, Daesh and the government come after you. If you work for Daesh, the government and the Taliban come for you. If you work by yourself in your field, one of them comes and says work for us, if you don't, they kill you."

They said they had family in the UK, and that they would keep trying to cross the Channel to join them.

"France is no good. The police beat us," said Ahmed. "We need to go to England."

I asked if they knew any UK politicians. This time, no conferring was needed. In unison and with big grins, they all shouted. "Sadiq Khan!"

"He's a good man, isn't he?" Said asked. The fact that a Muslim son of an immigrant could be elected to such high office had given them hope - the government might be hostile towards immigrants, but many of the people are not.

Their view of the attitudes of the British public chimes with the results of Amnesty's poll - nearly half of Britons would accept a refugee as a neighbour, almost a third of us would go as far as welcoming a refugee into our home.

Next week, presidents and prime ministers will meet at the World Humanitarian Summit in Istanbul to discuss a response to the refugee crisis. It is a global problem that needs a global solution, and governments must commit to a permanent system for sharing responsibility for hosting and assisting refugees, including providing safe and legal routes to sanctuary and ensuring that separated families are reunited. I hope David Cameron is listening to what the public is saying.